The mechanical properties of a machine manage power to achieve desired forces and movement. A machine consists of a power source and actuators that generate forces and movement, and a system of mechanisms that shape the actuator input to achieve a specific application of output forces and movement. Modern machines often include computers and sensors that monitor performance and plan movement, and are called mechanical systems.
The meaning of the word "machine" is traced by the Oxford English Dictionary[1] to an independently functioning structure and by Merriam-Webster Dictionary[2] to something that has been constructed. This includes human design into the meaning of machine.
The adjective "mechanical" refers to skill in the practical application of an art or science, as well as relating to or caused by movement, physical forces, properties or agents such as is dealt with by mechanics.[1] Similarly Merriam-Webster Dictionary[3] defines "mechanical" as relating to machinery or tools.
Power flow through a machine provides a way to understand the performance of devices ranging from levers and gear trains to automobiles and robotic systems. The German mechanician Franz Reuleaux[4] wrote "a machine is a combination of resistant bodies so arranged that by their means the mechanical forces of nature can be compelled to do work accompanied by certain determinate motion." Notice that forces and motion combine to define power.
More recently, Uicker et al.[5] state that a machine is "a device for applying power or changing its direction." And McCarthy and Soh[6] describe a machine as a system that "generally consists of a power source and a mechanism for the controlled use of this power."
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The idea that a machine can be decomposed into simple movable elements led Archimedes to define the lever, pulley and screw as simple machines. By the time of the Renaissance this list increased to include the wheel and axle, wedge and inclined plane. The modern approach to characterizing machines focusses on the components that allow movement, known as joints.
Wedge (hand axe): Perhaps the first example of a device designed to manage power is the hand axe, also see biface and Olorgesailie. A hand axe is made by chipping stone, generally flint, to form a bifacial edge, or wedge. A wedge is a simple machine that transforms lateral force and movement of the tool into a transverse splitting force and movement of the workpiece. The available power is limited by the effort of the person using the tool, but because power is the product of force and movement, the wedge amplifies the force by reducing the movement. This amplification, or mechanical advantage is the ratio of the input speed to output speed. For a wedge this is given by 1/tanα, where α is the tip angle. The faces of a wedge are modeled as straight lines to form a sliding or prismatic joint.
Lever: The lever is another important and simple device for managing power. This is a body that pivots on a fulcrum. Because the velocity of a point farther from the pivot is greater than the velocity of a point near the pivot, forces applied far from the pivot are amplified near the pivot by the associated decrease in speed. If a is the distance from the pivot to the point where the input force is applied and b is the distance to the point where the output force is applied, then a/b is the mechanical advantage of the lever. The fulcrum of a lever is modeled as a hinged or revolute joint.
Wheel: The wheel is clearly an important early machine, such as the chariot. A wheel uses the law of the lever to reduce the force needed to overcome friction when pulling a load. To see this notice that the friction associated with pulling a load on the ground is approximately the same as the friction in a simple bearing that supports the load on the axle of a wheel. However, the wheel forms a lever that magnifies the pulling force so that it overcomes the frictional resistance in the bearing.
Natural forces such as wind and water powered larger mechanical systems. Waterwheels appeared around the world around 300 BC to use flowing water to generate rotary motion, which was applied to milling grain, and powering lumber, machining and textile operations. Modern water turbines use water flowing through a dam to drive an electric generator. Early windmills captured wind power to generate rotary motion for milling operations. Modern wind turbines also drives a generator. This electricity in turn is used to drive motors forming the actuators of mechanical systems.
The word engine derives from "ingenuity" and originally referred to contrivances that may or may not be physical devices. See Merriam-Webster's definition of engine. A steam engine uses heat to boil water contained in a pressure vessel; the expanding steam drives a piston or a turbine. This principle can be seen in the aeolipile of Hero of Alexandria. This is called an external combustion engine.
An automobile engine is called an internal combustion engine because it burns fuel (an exothermic chemical reaction) inside a cylinder and uses the expanding gases to drive a piston. A jet engine uses a turbine to compress air which is burned with fuel so that it expands through a nozzle to provide thrust to an aircraft, and so is also an "internal combustion engine." [7]
The heat from coal and natural gas combustion in a boiler generates steam that drives a steam turbine to rotate an electric generator. A nuclear power plant uses heat from a nuclear reactor to generate steam and electric power. This power is distributed through a network of transmission lines for industrial and individual use. Electric motors use either AC or DC electric current to generate rotational movement. Electric servomotors are the actuators for mechanical systems ranging from robotic systems to modern aircraft. Hydraulic and pneumatic systems use electrically driven pumps to drive water or air respectively into cylinders to power linear movement.
A machine consists of an actuator input, a system of mechanisms that generate the output forces and movement, and an interface to the user. Electric motors, hydraulic and pneumatic actuators provide the input forces and movement. This input is shaped by mechanisms consisting of gears and gear trains, belt and chain drives, cam and follower mechanisms, and linkages as well as friction devices such as brakes and clutches. Structural components consist of the frame, fasteners, bearings, springs, lubricants and seals, as well as a variety of specialized machine elements such as splines, pins and keys.[4][5] The user interface ranges from switches and buttons to programmable logic controllers and includes the covers that provide texture, color and styling.
The transmission of rotation between contacting toothed wheels can be traced back to the Antikythera mechanism of Greece and the South Pointing Chariot of China. Illustrations by the renaissance scientist Georgius Agricola show gear trains with cylindrical teeth. The implementation of the involute tooth yielded a standard gear design that provides a constant speed ratio. Some important features of gears and gear trains are:
A cam and follower is formed by the direct contact of two specially shaped links. The driving link is called the cam (also see cam shaft) and the link that is driven through the direct contact of their surfaces is called the follower. The shape of the contacting surfaces of the cam and follower determines the movement of the mechanism.
A linkage is a collection of links connected by joints. Generally, the links are the structural elements and the joints allow movement. Perhaps the single most useful example is the planar four-bar linkage. However, there are many more special linkages:
A flexure mechanism consisted of a series of rigid bodies connected by compliant elements (also known as flexure joints) that is designed to produce a geometrically well-defined motion upon application of a force.
A number of machine elements provide important structural functions such as the frame, bearings, splines, spring and seals.
Usher[8] reports that Hero of Alexandria's treatise on Mechanics focussed on the study of lifting heavy weights. Today mechanics refers to the mathematical analysis of the forces and movement of a mechanical system, and consists of the study of the kinematics and dynamics of these systems.
Kinematics applies geometry to the analysis of movement in a mechanical system. The rotation and sliding movement central to mechanical systems are modeled mathematically as Euclidean, or rigid, transformations. The set of rigid transformations in three dimensional space forms a Lie group, denoted as SE(3).
Planar mechanisms: While all mechanisms in a mechanical system are three dimensional, they can be analyzed using plane geometry, if the movement of the individual components are constrained so all point trajectories are parallel to a plane. In this case the system is called a planar mechanism. The kinematic analysis of planar mechanisms uses the subset of SE(3) consisting of planar rotations and translations, denote SE(2).
The group SE(2) is three dimensional, which means that every position of a body in the plane is defined by three parameters. The parameters are often the x and y coordinates of the origin of a coordinate frame in M measured from the origin of a coordinate frame in F, and the angle measured from the x-axis in F to the x-axis in M. This is often described saying a body in the plane has three degrees-of-freedom.
The pure rotation of a hinge and the linear translation of a slider can be identified with subgroups of SE(2), and define the two joints one degree-of-freedom joints of planar mechanisms. The cam joint formed by two surfaces in sliding and rotating contact is a two degree-of-freedom joint.
Select this link to see Theo Jansen's Strandbeest walking machine with legs constructed from planar eight-bar linkages
Spherical mechanisms: It is possible to construct a mechanism such that the point trajectories in all components lie in concentric spherical shells around a fixed point. An example is the gimbaled gyroscope. These devices are called spherical mechanisms.[6] Spherical mechanisms are constructed by connecting links with hinged joints such that the axes of each hinge passes through the same point. This point becomes center of the concentric spherical shells. The movement of these mechanisms is characterized by the group SO(3) of rotations in three dimensional space. Other examples of spherical mechanisms are the automotive differential and the robotic wrist.
Select this link for an animation of a Spherical deployable mechanism.
The rotation group SO(3) is three dimensional. An example of the three parameters that specify a spatial rotation are the roll, pitch and yaw angles used to define the orientation of an aircraft.
Spatial mechanisms: A mechanism in which a body moves through a general spatial movement is called a spatial mechanism. An example is the RSSR linkage, which can be viewed as a four-bar linkage in which the hinged joints of the coupler link are replaced by rod ends, also called spherical joints or ball joints. The rod ends allow the input and output cranks of the RSSR linkage to be misaligned to the point that they lie in different planes, which causes the coupler link to move in a general spatial movement. Robot arms, Stewart platforms, and humanoid robotic systems are also examples of spatial mechanisms.
Select this link for an animation of Bennett's linkage, which is a spatial mechanism constructed from four hinged joints.
The group SE(3) is six dimensional, which means the position of a body in space is defined by six parameters. Three of the parameters define the origin of the moving reference frame relative to the fixed frame. Three other parameters define the orientation of the moving frame relative to the fixed frame.